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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/optimization/optimization_ex2" target="_blank">Open optimization_ex2 in new tab.</a>
<a name="output"></a>
<br><br><br> <h1> The console output of the program: </h1>
<pre>
***************************************************************
* Running Example optimization_ex2:
*   example-opt -tao_monitor -tao_view -tao_type ipm -pc_type jacobi -ksp_max_it 100
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=441
    n_local_nodes()=441
  n_elem()=100
    n_local_elem()=100
    n_active_elem()=100
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "Optimization"
    Type "Optimization"
    Variables="u"
    Finite Element Types="LAGRANGE", "JACOBI_20_00"
    Infinite Element Mapping="CARTESIAN"
    Approximation Orders="SECOND", "THIRD"
    n_dofs()=441
    n_local_dofs()=441
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=4
    n_matrices()=2
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 14.8776
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 25
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

iter =   1, Function value: 0,  Residual: 297167
iter =   1, Function value: 9268.21,  Residual: 46796.6
iter =   2, Function value: 20398.4,  Residual: 48161.3
iter =   3, Function value: 20168.2,  Residual: 47947.4
iter =   4, Function value: 20696.5,  Residual: 47351.4
iter =   5, Function value: 20699.9,  Residual: 47349.1
iter =   6, Function value: 20699.9,  Residual: 47349.1
iter =   7, Function value: 20699.9,  Residual: 47349.1
iter =   8, Function value: 20699.9,  Residual: 47349.1
iter =   9, Function value: 20699.9,  Residual: 47349.1
iter =  10, Function value: 20699.9,  Residual: 47349.1
iter =  11, Function value: 20699.9,  Residual: 47349.1
iter =  12, Function value: 20699.9,  Residual: 47349.1
iter =  13, Function value: 20699.9,  Residual: 47349.1
iter =  14, Function value: 20699.9,  Residual: 47349.1
iter =  15, Function value: 20699.9,  Residual: 47349.1
iter =  16, Function value: 20699.9,  Residual: 47349.1
iter =  17, Function value: 20699.9,  Residual: 47349.1
iter =  18, Function value: 20699.9,  Residual: 47349.1
iter =  19, Function value: 20699.9,  Residual: 47349.1
iter =  20, Function value: 20699.9,  Residual: 47349.1
iter =  21, Function value: 20699.9,  Residual: 47349.1
iter =  22, Function value: 20699.9,  Residual: 47349.1
iter =  23, Function value: 20699.9,  Residual: 47349.1
iter =  24, Function value: 20699.9,  Residual: 47349.1
iter =  25, Function value: 20699.9,  Residual: 47349.1
iter =  26, Function value: 20699.9,  Residual: 47349.1
iter =  27, Function value: 20699.9,  Residual: 47349.1
iter =  28, Function value: 20699.9,  Residual: 47349.1
iter =  29, Function value: 20699.9,  Residual: 47349.1
iter =  30, Function value: 20699.9,  Residual: 47349.1
iter =  31, Function value: 20699.9,  Residual: 47349.1
iter =  32, Function value: 20699.9,  Residual: 47349.1
iter =  33, Function value: 20699.9,  Residual: 47349.1
iter =  34, Function value: 20699.9,  Residual: 47349.1
iter =  35, Function value: 20699.9,  Residual: 47349.1
iter =  36, Function value: 20699.9,  Residual: 47349.1
iter =  37, Function value: 20699.9,  Residual: 47349.1
iter =  38, Function value: 20699.9,  Residual: 47349.1
iter =  39, Function value: 20699.9,  Residual: 47349.1
iter =  40, Function value: 20699.9,  Residual: 47349.1
iter =  41, Function value: 20699.9,  Residual: 47349.1
iter =  42, Function value: 20699.9,  Residual: 47349.1
iter =  43, Function value: 20699.9,  Residual: 47349.1
iter =  44, Function value: 20699.9,  Residual: 47349.1
iter =  45, Function value: 20699.9,  Residual: 47349.1
iter =  46, Function value: 20699.9,  Residual: 47349.1
iter =  47, Function value: 20699.9,  Residual: 47349.1
iter =  48, Function value: 20699.9,  Residual: 47349.1
iter =  49, Function value: 20699.9,  Residual: 47349.1
iter =  50, Function value: 20699.9,  Residual: 47349.1
iter =  51, Function value: 20699.9,  Residual: 47349.1
iter =  52, Function value: 20699.9,  Residual: 47349.1
iter =  53, Function value: 20699.9,  Residual: 47349.1
iter =  54, Function value: 20699.9,  Residual: 47349.1
iter =  55, Function value: 20699.9,  Residual: 47349.1
iter =  56, Function value: 20699.9,  Residual: 47349.1
iter =  57, Function value: 20699.9,  Residual: 47349.1
iter =  58, Function value: 20699.9,  Residual: 47349.1
iter =  59, Function value: 20699.9,  Residual: 47349.1
iter =  60, Function value: 20699.9,  Residual: 47349.1
iter =  61, Function value: 20699.9,  Residual: 47349.1
iter =  62, Function value: 20699.9,  Residual: 47349.1
iter =  63, Function value: 20699.9,  Residual: 47349.1
iter =  64, Function value: 20699.9,  Residual: 47349.1
iter =  65, Function value: 20699.9,  Residual: 47349.1
iter =  66, Function value: 20699.9,  Residual: 47349.1
iter =  67, Function value: 20699.9,  Residual: 47349.1
iter =  68, Function value: 20699.9,  Residual: 47349.1
iter =  69, Function value: 20699.9,  Residual: 47349.1
iter =  70, Function value: 20699.9,  Residual: 47349.1
iter =  71, Function value: 20699.9,  Residual: 47349.1
iter =  72, Function value: 20699.9,  Residual: 47349.1
iter =  73, Function value: 20699.9,  Residual: 47349.1
iter =  74, Function value: 20699.9,  Residual: 47349.1
iter =  75, Function value: 20699.9,  Residual: 47349.1
iter =  76, Function value: 20699.9,  Residual: 47349.1
iter =  77, Function value: 20699.9,  Residual: 47349.1
iter =  78, Function value: 20699.9,  Residual: 47349.1
iter =  79, Function value: 20699.9,  Residual: 47349.1
iter =  80, Function value: 20699.9,  Residual: 47349.1
iter =  81, Function value: 20699.9,  Residual: 47349.1
iter =  82, Function value: 20699.9,  Residual: 47349.1
iter =  83, Function value: 20699.9,  Residual: 47349.1
iter =  84, Function value: 20699.9,  Residual: 47349.1
iter =  85, Function value: 20699.9,  Residual: 47349.1
iter =  86, Function value: 20699.9,  Residual: 47349.1
iter =  87, Function value: 20699.9,  Residual: 47349.1
iter =  88, Function value: 20699.9,  Residual: 47349.1
iter =  89, Function value: 20699.9,  Residual: 47349.1
iter =  90, Function value: 20699.9,  Residual: 47349.1
iter =  91, Function value: 20699.9,  Residual: 47349.1
iter =  92, Function value: 20699.9,  Residual: 47349.1
iter =  93, Function value: 20699.9,  Residual: 47349.1
iter =  94, Function value: 20699.9,  Residual: 47349.1
iter =  95, Function value: 20699.9,  Residual: 47349.1
iter =  96, Function value: 20699.9,  Residual: 47349.1
iter =  97, Function value: 20699.9,  Residual: 47349.1
iter =  98, Function value: 20699.9,  Residual: 47349.1
iter =  99, Function value: 20699.9,  Residual: 47349.1
iter = 100, Function value: 20699.9,  Residual: 47349.1
iter = 101, Function value: 20699.9,  Residual: 47349.1
iter = 102, Function value: 20699.9,  Residual: 47349.1
iter = 103, Function value: 20699.9,  Residual: 47349.1
iter = 104, Function value: 20699.9,  Residual: 47349.1
iter = 105, Function value: 20699.9,  Residual: 47349.1
iter = 106, Function value: 20699.9,  Residual: 47349.1
iter = 107, Function value: 20699.9,  Residual: 47349.1
iter = 108, Function value: 20699.9,  Residual: 47349.1
iter = 109, Function value: 20699.9,  Residual: 47349.1
iter = 110, Function value: 20699.9,  Residual: 47349.1
iter = 111, Function value: 20699.9,  Residual: 47349.1
iter = 112, Function value: 20699.9,  Residual: 47349.1
iter = 113, Function value: 20699.9,  Residual: 47349.1
iter = 114, Function value: 20699.9,  Residual: 47349.1
iter = 115, Function value: 20699.9,  Residual: 47349.1
iter = 116, Function value: 20699.9,  Residual: 47349.1
iter = 117, Function value: 20699.9,  Residual: 47349.1
iter = 118, Function value: 20699.9,  Residual: 47349.1
iter = 119, Function value: 20699.9,  Residual: 47349.1
iter = 120, Function value: 20699.9,  Residual: 47349.1
iter = 121, Function value: 20699.9,  Residual: 47349.1
iter = 122, Function value: 20699.9,  Residual: 47349.1
iter = 123, Function value: 20699.9,  Residual: 47349.1
iter = 124, Function value: 20699.9,  Residual: 47349.1
iter = 125, Function value: 20699.9,  Residual: 47349.1
iter = 126, Function value: 20699.9,  Residual: 47349.1
iter = 127, Function value: 20699.9,  Residual: 47349.1
iter = 128, Function value: 20699.9,  Residual: 47349.1
Tao Object: 1 MPI processes
  type: ipm
  KSP Object:   1 MPI processes
    type: gmres
  total KSP iterations: 25600
  Active Set subset type: subvec
  convergence tolerances: fatol=0.0001,   frtol=0.0001
  convergence tolerances: gatol=1e-08,   steptol=0,   gttol=0
  Residual in Function/Gradient:=47349.1
  Objective value=20699.9
  total number of iterations=129,                          (max: 200)
  total number of function evaluations=129,                  max: 128
  total number of gradient evaluations=129,                  max: 128
  total number of Hessian evaluations=129
  total number of constraint function evaluations=258
  Solver terminated: -5   Maximum Function Evaluations
Tao optimization solver convergence/divergence reason: DIVERGED_LS_FAILURE

 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 09:41:43 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 ------------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.910295, Active time=0.902392                                                   |
 ------------------------------------------------------------------------------------------------------------------
| Event                               nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                                w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|------------------------------------------------------------------------------------------------------------------|
|                                                                                                                  |
|                                                                                                                  |
| DofMap                                                                                                           |
|   add_neighbors_to_send_list()      1          0.0000      0.000033    0.0000      0.000033    0.00     0.00     |
|   build_sparsity()                  1          0.0003      0.000256    0.0003      0.000291    0.03     0.03     |
|   create_dof_constraints()          1          0.0000      0.000015    0.0000      0.000015    0.00     0.00     |
|   distribute_dofs()                 1          0.0001      0.000057    0.0002      0.000241    0.01     0.03     |
|   dof_indices()                     200        0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   prepare_send_list()               2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                          1          0.0002      0.000183    0.0002      0.000183    0.02     0.02     |
|                                                                                                                  |
| FE                                                                                                               |
|   compute_shape_functions()         100        0.0002      0.000002    0.0002      0.000002    0.02     0.02     |
|   init_shape_functions()            1          0.0000      0.000012    0.0000      0.000012    0.00     0.00     |
|                                                                                                                  |
| FEMap                                                                                                            |
|   compute_affine_map()              100        0.0001      0.000001    0.0001      0.000001    0.01     0.01     |
|   init_reference_to_physical_map()  1          0.0000      0.000016    0.0000      0.000016    0.00     0.00     |
|                                                                                                                  |
| Mesh                                                                                                             |
|   find_neighbors()                  1          0.0002      0.000180    0.0002      0.000180    0.02     0.02     |
|   renumber_nodes_and_elem()         2          0.0000      0.000004    0.0000      0.000004    0.00     0.00     |
|                                                                                                                  |
| MeshTools::Generation                                                                                            |
|   build_cube()                      1          0.0001      0.000091    0.0001      0.000091    0.01     0.01     |
|                                                                                                                  |
| OptimizationSystem                                                                                               |
|   solve()                           1          0.0001      0.000051    0.9013      0.901288    0.01     99.88    |
|                                                                                                                  |
| Parallel                                                                                                         |
|   allgather()                       1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                  |
| Partitioner                                                                                                      |
|   single_partition()                1          0.0000      0.000009    0.0000      0.000009    0.00     0.00     |
|                                                                                                                  |
| TaoOptimizationSolver                                                                                            |
|   equality_constraints()            129        0.0022      0.000017    0.0022      0.000017    0.24     0.24     |
|   equality_constraints_jacobian()   129        0.0007      0.000005    0.0007      0.000005    0.08     0.08     |
|   get_dual_variables()              129        0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   gradient()                        129        0.0020      0.000015    0.0020      0.000015    0.22     0.22     |
|   hessian()                         129        0.0198      0.000154    0.0198      0.000154    2.20     2.20     |
|   inequality_constraints()          129        0.0016      0.000013    0.0016      0.000013    0.18     0.18     |
|   inequality_constraints_jacobian() 129        0.0015      0.000011    0.0015      0.000011    0.16     0.16     |
|   objective()                       129        0.0031      0.000024    0.0031      0.000024    0.34     0.34     |
|   solve()                           1          0.8703      0.870275    0.9012      0.901237    96.44    99.87    |
 ------------------------------------------------------------------------------------------------------------------
| Totals:                             1449       0.9024                                          100.00            |
 ------------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example optimization_ex2:
*   example-opt -tao_monitor -tao_view -tao_type ipm -pc_type jacobi -ksp_max_it 100
***************************************************************
</pre>
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